Explore a comprehensive lecture on mean-field limits for quantum systems and nonlinear Gibbs measures presented by Mathieu Lewin at the International Mathematical Union. Delve into the complex world of quantum particle systems, starting with the linear Schrödinger equation in R^{3N} and progressing to the limit as N approaches infinity. Discover how Bose-Einstein condensation emerges and learn about the quantum de Finetti theorem, which explains how independence arises from symmetry. Investigate the appearance of nonlinear Gibbs measures in systems with increased randomness and their significance in various mathematical fields. Examine topics such as mean-field limits, Bose-Einstein condensates, convergence of minimum, quantum de Finetti, nonlinear Gibbs measures, and renormalization techniques. Access accompanying slides for visual support and deeper understanding of this advanced mathematical exploration.